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C₃×D₃×B(4,𝔽₂) #11865243

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁷

Aliases

C₃×D₃×B(4,𝔽₂)

Splittings

Fitting	C₃²×B(4,𝔽₂) ⋊ C₂
Sylow	C₃² ⋊ C₂×B(4,𝔽₂)

Subgroups

	subgroup	G/H
center	C₂×C₃	D₃×#120
commutator, cosocle	C₂³×C₃	C₂⁴×C₃
Frattini	C₂³	C₂³×C₃×D₃
Fitting	C₃²×B(4,𝔽₂)	C₂
socle	C₂×C₃²	C₂×#120
hypercenter	C₃×B(4,𝔽₂)	D₃
hypocenter	C₃	C₂×C₃×B(4,𝔽₂)
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂³×C₃ ◁ C₃×B(4,𝔽₂)

2135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,ℤ/9)×B(4,𝔽₂), C₃×#11865254, C₃×D₃×#1020⋊C₂, …
maximal normal subgroup of	D₃²×B(4,𝔽₂), C₂×C₃×D₃×B(4,𝔽₂)
maximal quotient of	AGL(1,ℤ/9)×B(4,𝔽₂), C₃×#11865254, C₃×D₃×#5032, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 99254);